Figure. The minimum-bias values of v2, v4, and v6 with respect to the second harmonic event plane as a function of transverse momentum. The v2 values have been divided by a factor of two to fit on scale. Also shown are the three-particle cumulant values (triangles) for v4 (v4{3}). The dashed curves are 1.2 v22 and 1.2 v23

This is the first measurement of higher harmonics of the momentum anisotropy at RHIC, and it is expected that these higher harmonics will be a sensitive test of the initial configuration of the system, since they provide a Fourier analysis of the shape in momentum space which can be related back to the initial shape in position space.

The results as a function of transverse momentum are shown in the figure for minimum bias collisions (0 - 80% centrality). Shown for v₄ are both the analysis relative to the second harmonic event plane, v₄{EP₂}, and the three-particle cumulant, v₄{3}. Both methods determine the sign of v₄ to be positive. As a function of p_t, v₄ rises more slowly from the origin than v₂, but does flatten out at high p_t like v₂. The v₆(p_t) values are consistent with zero.

It has proposed that for the higher harmonics, v_n might be proportional to v₂^n/2. In order to test the applicability of this scaling, we have also plotted v₂² and v₂³ in the figure as dashed lines. The proportionality constant has been taken to be 1.2 in order to fit the v₄ data. The fit is good, and v₆, although essentially zero, is not inconsistent with scaling as v₂³.